Lagrange identity for polynomials and -codes of lengths and

Author:
C. H. Yang

Journal:
Proc. Amer. Math. Soc. **88** (1983), 746-750

MSC:
Primary 05B20; Secondary 05A19, 94B99

MathSciNet review:
702312

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Abstract: It is known that application of the Lagrange identity for polynomials (see [**1**]) is the key to composing four-symbol -codes of length for and odd or , where , , , , and are nonnegative integers. Applications of the Lagrange identity also lead to constructions of four-symbol -codes of length for or . Consequently, new families of Hadamard matrices of orders and can be constructed, where is the order of Williamson matrices. Related topics on zero correlation codes are also discussed.

**[1]**C. H. Yang,*A composition theorem for**-codes*(to appear).**[2]**C. H. Yang,*Hadamard matrices and 𝛿-codes of length 3𝑛*, Proc. Amer. Math. Soc.**85**(1982), no. 3, 480–482. MR**656128**, 10.1090/S0002-9939-1982-0656128-3**[3]**C. H. Yang,*Hadamard matrices, finite sequences, and polynomials defined on the unit circle*, Math. Comp.**33**(1979), no. 146, 688–693. MR**525685**, 10.1090/S0025-5718-1979-0525685-8**[4]**R. J. Turyn,*Hadamard matrices, Baumert-Hall units, four-symbol sequences, pulse compression, and surface wave encodings*, J. Combinatorial Theory Ser. A**16**(1974), 313–333. MR**0345847****[5]**-,*Computation of certain Hadamard matrices*, Notices Amer. Math. Soc.**20**(1973), A-l.

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DOI:
https://doi.org/10.1090/S0002-9939-1983-0702312-0

Article copyright:
© Copyright 1983
American Mathematical Society